ISTANBUL—Turkey’s parliament voted on Thursday to expand the government’s authority to order cross-border military operations, as Syrian Kurdish militia warned that Islamic State insurgents were close to overrunning a strategic town near the border.

Syrian Kurdish commanders in the besieged town of Ayn al-Arab, known as Kobani in Kurdish, said jihadist fighters had advanced to within just over a mile of the town despite coalition airstrikes on Wednesday intended to weaken them. The Syrian Observatory for Human Rights, a...